Retrieval of ice cloud properties using an optimal estimation algorithm and MODIS infrared observations. Part I: Forward model, error analysis, and information content.

An optimal estimation (OE) retrieval method is developed to infer three ice cloud properties simultaneously: optical thickness (τ), effective radius (reff ), and cloud-top height (h). This method is based on a fast radiative transfer (RT) model and infrared (IR) observations from the MODerate resolution Imaging Spectroradiometer (MODIS). This study conducts thorough error and information content analyses to understand the error propagation and performance of retrievals from various MODIS band combinations under different cloud/atmosphere states. Specifically, the algorithm takes into account four error sources: measurement uncertainty, fast RT model uncertainty, uncertainties in ancillary datasets (e.g., atmospheric state), and assumed ice crystal habit uncertainties. It is found that the ancillary and ice crystal habit error sources dominate the MODIS IR retrieval uncertainty and cannot be ignored. The information content analysis shows that, for a given ice cloud, the use of four MODIS IR observations is sufficient to retrieve the three cloud properties. However, the selection of MODIS IR bands that provide the most information and their order of importance varies with both the ice cloud properties and the ambient atmospheric and the surface states. As a result, this study suggests the inclusion of all MODIS IR bands in practice since little a priori information is available.